PNRPU Mechanics Bulletin最新文献

{"title":"Plane-Strain Extrusion of a Green Type Porous Plastic Material through a Wedge-Shaped Die","authors":"G. Sevastyanov","doi":"10.15593/perm.mech/2022.2.01","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.2.01","url":null,"abstract":", Gurson criterion, plane-strain condition, wedge-shaped die. This paper presents the solutions for the plane-strain extrusion of porous material. We consider the problem of a stationary plastic flow through a wedge shaped die. We neglect friction between the die and the deformed material since it is rather a negative effect and should be avoided in manufacturing. The elliptic Green type yield condition and its piecewise-linear approximation are adopted for this problem. In the last case, we obtain analytical solution that links extrusion pressure and area reduction to the initial and final density of the porous material. For elliptic Green yield condition the problem reduced to nonlinear ODE that integrated numerically. The results are compared with known solution for Gurson model. The extrusion pressure predicted by the piecewise-linear model is lower than what obtained by the elliptic Green model. In turn, the pressure predicted by elliptic Green model is lower than the pressure obtained in the frame of Gurson model. At low values of area reduction, all three models predict approximately the same extrusion pressure. With a small initial porosity of the material, the Gurson model gives results that are close to the elliptic Green model, and with a large initial porosity, to the piece-wise-linear Green model. © PNRPU","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46067335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"EFFECT OF SYNCHRONIZATION OF CONTINUOUS ACOUSTIC EMISSION STATISTICAL PROPERTIES DURING STRUCTURALLY HETEROGENEOUS MATERIALS DEFORMATION","authors":"I. Panteleev, Y. Bayandin, O. Plekhov","doi":"10.15593/perm.mech/2022.3.01","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.3.01","url":null,"abstract":"In this paper, a correlation analysis of the statistical properties of continuous acoustic emission recorded in various parts of marble and glass fiber laminate samples during their quasi-static deformation is carried out. The spectral measure of coherence, which is a generalization of the square modulus of the coherence spectrum to the case of multidimensional series, is chosen as a correlation measure. The measure of coherence was estimated for the width of the multifractal spectrum and the spectrum carrier realizing its maximum, calculated in a sliding time window for acoustic emission signals. It is shown that the preparation of a macrofracture site is accompanied by synchronization of the statistical properties of acoustic emission in the selected frequency intervals. Based on the analysis of changes in the frequency-averaged measure of coherence for both types of materials, four characteristic stages are distinguished, the boundaries of which are individual for each of the materials. The onset of the fourth stage, which is characterized by a monotonic increase in the average measure of the coherence of the statistical properties of the AE, can be chosen as a possible criterion for the transition of the material to the limiting state.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47298097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical simulation of the nickel alloy microstructure formed in the process of hot fogging","authors":"","doi":"10.15593/perm.mech/2022.3.14","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.3.14","url":null,"abstract":"The paper presents a comprehensive analysis of the deformation and thermal states of the Waspaloy alloy billet heated to different initial temperatures of 1100°C and 1150°C and subjected to free upsetting to an average diameter of ~1060 mm at the deformation rate of 100 mm/s. The thermodynamic forces acting on the billet trigger the process of dynamic recrystallization, which is associated with the appearance and growth of low-defect nuclei of new grains instead of the deformed ones. To describe the material microstructure evolution, the phenomenological approach implemented in the DEFORM-2D/3D software package was applied. The simulation was based on the modified Johnson - Mehl - Avrami - Kolmogorov (JMAK) model, whose equations allow calculating the volume fraction of recrystallized material and describing the grain structure transformation of metal alloys. The results of solution of the non-stationary temperature problem are used to construct the temperature fields in the Waspaloy alloy billet during its transportation through air from the furnace to the deforming equipment within 45 seconds and during the subsequent upsetting process. For the latter, the force and strain characteristics, including the force required to complete this process, are determined in the framework of the plastic flow theory, and the characteristics of the grain structure of the nickel alloy, such as the average size of recrystallized grains and their volume fraction, are determined in the framework of the JMAK model. The results obtained by numerical simulation make it possible to substantiate an optimal selection of parameters of billet deformation ensuring the formation of the required material structure.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47868139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Contact problems for a transversely isotropic layer","authors":"D. Pozharskii, N. B. Zolotov","doi":"10.15593/perm.mech/2022.2.10","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.2.10","url":null,"abstract":"Two spatial, one axisymmetric and two plane contact problems are considered for a transversely isotropic elastic layer with one face subjected to sliding support. In the spatial and plane contact problems, the planes of isotropy may be either parallel or perpendicular to the layer faces. In the case of axial symmetry, the planes of isotropy are parallel to the layer faces. By using Fourier integral transforms, the contact problems are reduced to integral equations with respect to the contact pressure, the limiting cases of which are the well-known equations of the corresponding problems for an isotropic layer. For solving the spatial problems with unknown contact domains, the nonlinear boundary integral equations method is used, which make it possible to determine the contact pressure and the contact domain simultaneously. To extract the kernel principal part of the spatial problem integral equation when the isotropy planes are perpendicular to the layer faces, it is used the kernel of the integral equation of the corresponding contact problem for a transversely isotropic half-space obtained earlier without quadratures. The integral equation of the axially symmetric problem is reduced to a Fredholm integral equation of the second kind with the help of the method of pair equations, and the method of mechanical quadratures is used for numerical solutions. Plane problems are solved in a closed form based on special approximations of the kernel symbols. The approximations accuracy grows as anisotropy increases. Here, the anisotropy level can be characterized by the difference between ratio of a characteristic equation roots and unit because the unit value corresponds to the isotropic case. Mechanical characteristics as well as errors of the approximations are calculated for well-known transversely isotropic materials.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42494155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling of the elastoplastic deformation process of single crystal superalloys","authors":"","doi":"10.15593/perm.mech/2022.2.06","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.2.06","url":null,"abstract":"The aim of the research is the development and verification of a micromechanically motivated model of elastoplastic deformation of two-phase single-crystal nickel-based alloys, predicting behavior under high-temperature thermomechanical actionswith taking into account the presence of γ and γ' phases. The model is relevant for computations of the stress-strain state of cooled single crystal blades of gas turbine units. The constitutive equations for each of the phases took into account the anisotropy of elastic and plastic properties, the presence of octahedral slip systems, features of the cubic system, and various hardening mechanisms, including kinematic, isotropic and latent ones. The identification of the elastic and plastic constants of the material for the γ and γ 'phases was carried out on the basis of the known stress-strain curves for each phase. The determination of the effective properties and deformation diagrams of a two-phase single-crystal alloy, taking into account the presence of γ-γ'phases, was carried out both on the basis of finite element homogenization for the representative volume element, and using the simplest rheological (structural) models of the material, considering serial and parallel connection of phases. The dependences of the elastoplastic properties of two-phase single-crystal nickel-based alloys on the volume fraction of the γ'phase are determined by computational experiments and analytical estimates. In order to determine the optimal strategy for solving the class of problems under consideration, multivariant computational experiments were carried out for various types of boundary conditions of the homogenization problem, the number of periodicity cells, forms of inclusion of the γ'phase, volume fractions of the γ' phase, types of hardening, variants of rheological models and appropriate recommendations were given. The simulation results using the proposed two-level microstructural model of the material demonstrate a good agreement with the experimental data for the single-crystal superalloy CMSX-4.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43748498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Utilization of viscoelatic models with non-linear springs and dashpots in delamination study of multilayered beams","authors":"V. Ri̇zov","doi":"10.15593/perm.mech/2022.1.01","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.1.01","url":null,"abstract":"","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45499934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical model of oxide film deformation on the surface of a metallic melt in an alternating magnetic field","authors":"I. Nikulin, V. Demin","doi":"10.15593/perm.mech/2022.1.07","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.1.07","url":null,"abstract":"We consider a thin oxide film on the surface of a molten metal during induction melting. The alternating electromagnetic field excites eddy currents in the metal volume, which heat it, and Lorentz force, which causes the forced convection of the melt, the heating and the flows in the metal are discussed briefly. The contribution to the mechanical stresses in the film that gives the alternating electromagnetic field, the thermal expansion of the film, and the melt motion are considered in detail. The equations system describing magnetic field diffusion, equations of motion and heat transfer in the melt are written in the axisymmetric formulation. The corresponding boundary conditions are described, the governing dimensionless criteria, which determine the structure and intensity of the melt flow, including those at the surface where the film is located, are given. The film elastic deformation equation is derived from Hooke's law and written in terms of displacement in dimensional and dimensionless forms. On the base of literature review, the values of physical characteristics of the film, which are not available for direct measurement, are proposed. The verification of the mathematical model is given. Possible flows in the melt are calculated, taking into account the action of dynamic and thermal action of the film on the surface. The unambiguous relation of the film stress state with these flows is shown. The influence of the magnetic field diffusion parameter and the Hartmann number, which determine, respectively, the structure and intensity of the forced flow, on the film deformations is demonstrated. The mode map of regimes is constructed that relates the integral deformation of the film to the parameters of the magnetic field and the initial size of the film. It is found that the situations are possible when the film in the stress-strain state does not change its total size and remains in stable equilibrium on the surface of the moving melt. Recommendations for the usage of the presented results are given.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43473326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ON THE INFLUENCE OF THE MECHANICAL CHARACTERISTICS OF A THIN ADHESION LAYER ON THE COMPOSITE STRENGTH. PART 1. ELASTIC DEFORMATION","authors":"V. E. Bogacheva, V. Glagolev, L. V. Glagolev, A. Markin","doi":"10.15593/perm.mech/2022.3.12","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.3.12","url":null,"abstract":"The problem of deformation of a DCB sample, which is a composition of bodies bound by an adhesive layer of finite thickness, is considered. Based on the variational equilibrium equation containing the layer thickness as a linear parameter, a finite element solution of the problem of loading the layer with a normal discontinuity in the plane strain state is constructed. The stresses averaged over the layer thickness are related to the stresses along the layer boundary by the equilibrium equations. The boundary stresses of the layer form the boundary conditions for the mating bodies. In the layer, along with shear stresses, stresses orthogonal to shear are also taken into account. The constitutive relations in the layer are represented in terms of average stresses. With a significant difference in the Young's moduli of the adhesive and mating bodies, the convergence of the value of the J-integral with a decrease in the layer thickness is shown. To find the J-integral, its representation is used as a product of the specific free energy at the end of the layer and its thickness. It has been established that the Poisson's ratio of the bodies affects the value of the J-integral, and the Poisson's ratio of the adhesive layer has almost no effect on the value of the J-integral. Using the theory of plates Mindlin - Reisner at zero Poisson's ratio of the adhesive, an analytical representation of the J-integral is obtained. The representation includes energy terms related to the pull-off stress and the axial stress in the layer. In this case, the term associated with the axial stress in the layer is proportional to the square of the ratio of the Young's moduli of the adhesive layer and the bodies mating with it. From the solution obtained, it follows that the mechanical properties of the adhesive layer with a small thickness compared to bodies do not affect the value of the J-integral if the elastic modulus of the adhesive layer is significantly less than the elastic modulus of the mating bodies. Thus, the use of replacing the adhesive layer with a layer of zero thickness is correct under these restrictions.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42074053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of the limiting states of cylindrical elastic-plastic shells under tension and combined loading by internal pressure and tension","authors":"","doi":"10.15593/perm.mech/2022.2.04","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.2.04","url":null,"abstract":"The elastic-plastic deformation, limiting states and supercritical behavior of cylindrical shells under tension and combined loading by internal pressure and tension to failure are studied theoretically and experimentally. This problem is characterized by the occurrence of large strains, shape changes and, as a result, an inhomogeneous stress-strain state. In the numerical solution of such problems, the problem arises of constructing true stress-strain curves of materials. In this regard, to study the deformation and strength properties of materials, it is important to use an experimental-computational approach, which makes it possible to take into account the non-uniaxiality and inhomogeneous of the stress-strain state without accepting simplifying hypotheses. The paper presents a new efficient algorithm for constructing a true stress-strain curve, which is based on the procedure of nonlinear extrapolation of the curve. Such an algorithm, in the process of direct numerical solution of the problem, consistently constructs a stress-strain curve without using repeated direct calculations, which significantly (at times) increases its efficiency. Based on the experimental-computational approach, the true stress-strain curves for solid rods and shells made of 10KhSND and 10G2FBYu steels were determined under tension and combined loading by internal pressure and tension to failure. The failure of shells under tension occurs at lower (at times) values of true strain than solid rods. Significant differences in true stresses and strains at the moment of failure are due to different localization of deformation of solid rods and shells after the loss of stability of plastic deformation in tension. It is shown numerically and experimentally that after loss of stability of plastic deformation according to Considerer in tension, the cylindrical shell contains two forms of loss of stability until the moment of failure. The first form of loss of stability, as in solid rods, is characterized by localization of deformations along the diameter of the sample in the form of a neck, and the second form is characterized by localization of deformations along the thickness of the sample, which determines the final stage of failure. Under the action of internal pressure on the shell, the first form of loss of stability of plastic deformation degenerates with the formation of a neck inside the shell, and only the form of loss of stability is observed, caused by the localization of deformations along the thickness of the shell.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41789528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"REFINED DISCRETE METHOD FOR CALCULATING STIFFENED ORTHOTROPIC SHELLS","authors":"A. Semenov","doi":"10.15593/perm.mech/2022.4.09","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.4.09","url":null,"abstract":"The author proposes a refined discrete method for taking into account stiffeners in the simulationof thin-walled shell structures. According to the method, it is necessary to add different reduction factors along different coordinate axes. For ribs directed perpendicular to the considered direction, a reduction factor is introduced equal to the ratio of the width of the ribs in this direction to the linear size of the shell in the considered direction. This method supplements the previously developed geometrically nonlinear mathematical model, which takes into account transverse shears and material orthotropy. The model is written as a functional of the total potential strain energy and can be used for different types of shells by specifying the Lame parameters and the radii of principal curvatures. The computational algorithm is based on the Ritz method and the method of continuation of the solution with respect to the best parameter. The software imple-mentation was carried out in the Maple software package. The applicability of the refined discrete method is shown by the example of orthotropic shallow shells of double curvature, simply supported along the contour and under the action of an external uniformly distributed transverse load. Material parameters were selected for T-10/UPE22-27 and 0/90 Woven Roving E-Glass/Vinyl Ester fiberglass. A comparison was made of the values of critical buckling loads for different stiffening options (a grid of ribs from 0 to 12 ribs in each direction) and a comparison of the values with the conventional discrete method, which showed that with the conventional discrete method, the values of buckling loads are significantly overestimated, especially with an increase in the number stiffening ribs. Comparison of the results of the test problem with the results of experiments obtained by other authors showed good agreement between the refined discrete method.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42323302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}